Standard State Thermodynamic Properties Research Articles

Standard State Thermodynamic Properties of Completely Ionized Aqueous Sodium Sulfate Using High Dilution Calorimetry up to 598.15 K

Pabalan and Pitzer (Geochim. Cosmochim. Acta 1988, 52, 2393-2404) reported a comprehensive set of thermodynamic properties of aqueous solutions of sodium sulfate without using ion association or hydrolysis. However, there is now ample evidence available indicating that the ion association cannot be ignored at temperatures T>or=373 K. For example, even at the lowest concentration of their studies (m>or=0.05) and at 573.15 K, less than 20% of SO4(2-)(aq) is available as free ions. In the present study, the integral heats of solution of sodium sulfate were measured to very low concentrations (10(-4) m) up to 573.16 K. The data were analyzed correcting for the hydrolysis of SO4(2-)(aq) and the association of Na+(aq) with SO4(2-)(aq) and NaSO4-(aq) in order to obtain the final standard state thermodynamic properties of completely ionized aqueous sodium sulfate, Na2SO4(aq). From these and the available solubility data, the stoichiometric activity coefficients of saturated aqueous solutions of sodium sulfate were calculated up to 573.15 K and compared with literature data. The stoichiometric activity coefficients of aqueous solutions of sodium sulfate, as a function of temperature at all concentrations (0<or=m<or=msat), were also calculated up to 573.15 K.

Standard State Thermodynamic Properties of Completely Dissociated Hydrochloric Acid and Aqueous Sodium Hydroxide at Extreme Temperatures and Pressures

Standard state thermodynamic properties for completely dissociated hydrochloric acid were fixed by ionic additivity, using the data from other strong electrolytes perrhenic acid, sodium perrhenate, and sodium chloride from 298.15 to 598.15 K and at p(sat). The standard electrode potential for the important silver-silver chloride electrode system and the equilibrium constants for the volatility of HCl from aqueous solutions were then calculated and compared with literature data. Using the experimental data from this study and auxiliary data from literature, the logarithm of the molal association constant of HCl at the critical temperature of water and at 673.15 K up to 1000 MPa was predicted from the unified theory of electrolytes (UTE). The standard state thermodynamic properties for completely dissociated aqueous sodium hydroxide were also calculated by ionic additivity over the same temperature range from aqueous sodium chloride, hydrochloric acid, and the dissociation constant of water. The results were compared with literature data.

High dilution calorimetric determination of the standard state thermodynamic differences between the properties of H +(aq) and Na +(aq) up to 598.15 K

Standard state thermodynamic properties for fully ionized aqueous perrhenic acid at temperature in the range of (298.15 to 598.15) K and at p sat were determined by high dilution solution calorimetry (10 −4 m). A comparison of the standard state thermodynamic properties for fully ionized aqueous perrhenic acid, HReO 4 ( aq ) , and sodium perrhenate, NaReO 4 ( aq ) , establishes for the first time the quantitative values for the differences between H + ( aq ) and Na + ( aq ) from temperature of (298.15 to 598.15) K. Perrhenic acid is believed to be the first strong acid to be thermodynamically well characterized under standard state conditions to date from measurements down to 10 −4 m. The value of the Debye–Hückel limiting slope for enthalpies of dilution at temperature of 596.30 K of 122 ± 6 kJ · mol −3/2 · kg 1/2, obtained from the integral heats of solution measurement at various concentrations, is in good agreement with theoretical value in literature, 121 kJ · mol −3/2 · kg 1/2. This agreement verifies that HReO 4 ( aq ) obeys the simple limiting law for strong electrolytes. Many thermodynamic properties of soluble sodium electrolytes can now be converted to the corresponding acid form.

Standard state thermodynamic properties of aqueous sodium perrhenate using high dilution calorimetry up to 598.15 K

Standard state thermodynamic properties for aqueous sodium perrhenate at temperature in the range of (298.15 to 598.15) K and at p sat were determined by high dilution solution calorimetry down to 10 −4 m. Standard state partial molar heat capacities, C p , 2 ∘ , of aqueous sodium perrhenate calculated from present study are compared to literature values up to T = 398.15 K. The differences between C p , 2 ∘ of ReO 4 - ( aq ) and Cl −(aq) at lower temperature is much greater than that due to their internal molecular motions. Consequently, the perrhenate ion appears to have an ionic incomplete primary hydration shell as compared to the chloride ion. The ReO 4 - / Cl - difference in thermodynamic functions has now been well defined up to T = 598.15 K for other important high temperature calculations.

Standard state thermodynamic properties of aqueous cesium chloride using high dilution calorimetry up to 598.15 K

In this communication we report the calorimetric data for the standard state enthalpies of solution of cesium chloride obtained from low concentrations, down to (10 −3 m), integral heats of solution measurement up to temperature of 573.30 K and extrapolated to 598.15 K. From these data and the unified theory of electrolytes, the complete standard state thermodynamic properties ( H 2 ∘ , G 2 ∘ , C p , 2 ∘ , V 2 ∘ , ( ∂ V 2 ∘ / ∂ T ) p , ( ∂ V 2 ∘ / ∂ p ) T ) of aqueous cesium chloride were determined up to temperature of 598.15 K.

Standard State Thermodynamic Properties of Aqueous Sodium Chloride Using High Dilution Calorimetry at Extreme Temperatures and Pressures

In this communication, we report the first calorimetric data for the standard state enthalpies of a solution of sodium chloride obtained from high dilution, down to (10(-3) m), integral heats of solution measurements to 596.30 K. Although there are no comparable thermodynamic data available at such high dilutions in the literature, the present results for NaCl(aq) can be used for many thermodynamic studies by others to achieve a complete thermodynamic description of this key electrolyte over very wide ranges of concentration. From the recently developed unified theory of electrolytes, the experimental data from this study were used to predict Gibbs free energies of hydration of sodium chloride up to 1100 K. These Gibbs free energies of hydration at different pressures and densities compare well with reported values obtained from ab initio calculations by others.

Dissociation Constants and Thermodynamic Properties of Amines and Alkanolamines from (293 to 353) K

The dissociation constants of protonated 2-amino-2-ethyl-1,3-propanediol, 2-amino-2-methyl-1-propanol, diethylmonoethanolamine, diisopropanolamine, dimethylmonoethanolamine, monoethanolamine, 1-amino-2-propanol, methylmonoethanolamine, triethanolamine, and the first and the second dissociation constants of piperazine and hydroxyethylpiperazine have been determined by electromotive force measurements from (293 to 353) K. The dissociation constants of protonated triethylamine have been determined with the same technique from (293 to 333) K. The experimental results and derived values of the standard state thermodynamic properties are reported and compared to available literature values.

The standard state thermodynamic properties for completely ionized hydrochloric acid and ionization of water up to 523 K

In this communication we report calorimetric data for the standard state enthalpies of solution of α-Ba(OH) 2 in high dilution (10 −3 m) hydrochloric acid obtained from integral heats of solution measurements from temperatures of (333.55 to 516.64) K and extrapolated to 298.15 K. From previous studies in this laboratory on BaCl 2(aq) and auxiliary literature data, the standard state thermodynamic functions for completely ionized HCl(aq) can be determined. These new data are in good agreement and confirm our previously reported results on HCl(aq) from ionic additivity. The enthalpy of formation of solid α-Ba(OH) 2 at temperature of 298.15 K of −939.38 kJ · mol −1 can also be calculated from the present results. Values of the standard state heat capacity change for the ionization of water up to temperature of 523.15 K and at p sat were calculated from present results using the literature data for NaOH(aq) and NaCl(aq) obtained from high dilution calorimetric measurements.

Thermodynamic Properties of Aqueous Gadolinium Perrhenate and Gadolinium Chloride from High Dilution Calorimetry at Extreme Temperatures and Pressures

The heat of solution of solid cubic gadolinium oxide has been measured in noncomplexing perrhenic acid solutions at very high dilutions (10(-4) m) up to 596.30 K, from which the standard state thermodynamic properties of aqueous gadolinium perrhenate were determined up to 623.15 K. From the measured differences between similar properties of aqueous sodium chloride and perrhenate, thermodynamic properties for aqueous gadolinium chloride were obtained by ionic additivity. Data for the hydrolysis of Gd3+(aq) were obtained by separate determinations. The enthalpy of solution of gadolinium chloride at 623.15 K obtained from this research (-2.7 MJ mol(-1)) is apparently larger than any other recorded for a chemical reaction involving aqueous systems. Standard state partial molal heat capacities for ThCl4(aq) were predicted up to 623.15 K.

Dissociation constants and thermodynamic properties of alkanolamines

The dissociation constants of protonated 2-amino-2-ethyl-1,3-propanediol (AEPD), 2-amino-2-methyl-1-propanol (AMP), diethylmonoethanolamine (DEMEA), diisopropanolamine (DIPA), dimethylmonoethanolamine (DMMEA), monoethanolamine (MEA), 1-amino-2-propanol (MIPA), and methylmonoethanolamine (MMEA) have been determined by electromotive force measurements from (293 to 353) K. The experimental results and derived values of the standard state thermodynamic properties are reported.

Dissociation Constants and Thermodynamic Properties of Amino Acids Used in CO2 Absorption from (293 to 353) K

The second dissociation constants of the amino acids β-alanine, taurine, sarcosine, 6-aminohexanoic acid, dl-methionine, glycine, l-phenylalanine, and l-proline and the third dissociation constants of l-glutamic acid and l-aspartic acid have been determined from electromotive force measurements at temperatures from (293 to 353) K. Experimental results are reported and compared to literature values. Values of the standard state thermodynamic properties are derived from the experimental results and compared to the values of commercially available amines used as absorbents for CO2 capture.

Densities and Apparent Molar Volumes of NaOH(aq) to the Temperature 623 K and Pressure to 30 MPa

Densities of NaOH(aq) solutions with molalities between 0.033 and 6.047 mol⋅kg−1 were measured with a vibrating-tube densitometer at temperatures between 373 K and 623 K and pressures from near the saturation vapor pressure of water to 30 MPa. Apparent molar volumes, V φ, calculated from the measured densities in this work were well represented with the Pitzer ion-interaction treatment up to T = 523 K. Above that temperature the formation of ion pairs must be taken into account to describe correctly the molality dependence of V φ and for the reliable extrapolation of V φ to infinite dilution. Standard-state thermodynamic properties for the ion formation reaction were taken from recently published electrical conductivity measurements. A comparison with previous correlations of volumetric properties of NaOH(aq) is presented covering the full range of pressure and temperature.

Thermodynamic properties of the Tschermak solid solution in Fe-chlorite: Application to natural examples and possible role of oxidation

The standard-state thermodynamic properties of 14 Å Fe-amesite [Fe4Al4Si2O10(OH)8] were calcu­lated from the reequilibration experiments of Pana et al. (2005) and natural data bearing on the Fe-Mg partitioning between chlorite and chloritoid over a wide range of pressure (P). temperature (7), and rock composition. The combination of these data with the three-site mixing model and thermodynamic properties of daphnite proposed by Vidal et al. (2001) led us to reappraise the evolution of the Margules parameter WGAlFe with pressure and temperature. The new data [H0fFe-Am = -7607460 J/mol, .S0Fe-Am = 514.8 J/(mol·K), V0Fe-Am = 20.90 J/bar, WGAlFe = 1200 - 31T + 0.7(P - 1)] are compatible with all the natural data and reequilibration experiments, and in fair agreement with the results of synthesis. They are used to calculate the compositional evolution of chlorite with T. P, or αO2 at different bulk-system compositions. The calculated phase relations and chlorite compositions are compared with previous experiments conducted in the FeO-Al2O3-SiO2-H2O system. The addition of the Fe-amesite end-member increases the number of equilibria that can be calculated for any natural assemblage involving chlorite. Two independent equilibria are obtained for natural (Fe-Mg)-chlorite-quartz or diaspore assemblages. It is therefore possible to estimate metamorphic conditions for high-variance assemblages from the composition of chlorite. We discuss the reliability of such P-T estimates using natural chlorites oc­curring in low-pressure and low-temperature or medium- to high-pressure and temperature samples. Assuming that the proposed model and thermodynamic parameters are correct, these various natural data suggest that XFe3+ [= Fe3+/(Fe2+ + Fe3+)] in metamorphic chlorites is low (<0.1), whereas it can be as high as 0.3 in Si- and Mg-rich chlorites formed at low -P-T conditions.

The Stability of Fe-Mg Chlorites in Hydrothermal Solutions: Ii. Thermodynamic Properties

AbstractThe hydrothermal stabilities of a low-Fe clinochlore and a high-Mg chamosite, in the presence of kaolinite, were investigated recently at T ⩽ 200°C and Pv=PH2O (Aja and Small, 1999; Aja and Dyar, 2002). Standard state thermodynamic properties (S2980, ΔfH1,2980 and ΔfG1,2980) have been obtained for the two chlorites whose structural formulae are (Al2.33Fe1.002+Fe0.143+Ca0.02Mn0.01Ni0.02Cr0.01Mg8.40α0.07) (Si5.66Al2.34)O20(OH)16 and (Fe0.603+Fe5.432+Mg2.30Al2.98Mn0.05Ca0.03Zn0.01α0.60)(Si5.63Al2.37)O20(OH)16. For the low-Fe clinochlore, the respective thermochemical properties are 430 J mol−1 K−1, −8770.64±35.24 kJ mol−1, and −8120.54±32.63 kJ mol−1. ΔfH1,2980, ΔfG1,2980 and S2980, similarly obtained for the Windsor chamosite are −7851.29±23.14 kJ mol−1, −7271.01±21.43 kJ mol−1 and 668±5 J mol−1K−1, respectively. Ideal site-mixing models of chlorite composition, along the chamosite-clinochlore binary, fail to model satisfactorily these chlorite-fluid equilibria only at lower temperatures (T &lt;175°C). The magnitudes of the excess thermodynamic properties calculated for these chlorites, within the ternary clinochlore-daphnite-sudoite system, suggest significant deviations from ideality.

Magnetite surface charge studies to 290°C from in situ pH titrations

The proton-induced surface charge of magnetite was investigated in 0.03 and 0.30 molal sodium trifluoromethanesulfonate solutions from 25°C to 290°C by potentiometric titrations using a stirred hydrogen electrode concentration cell. Pure magnetite with excellent crystallinity was produced by reaction with the Ni/NiO/H 2O hydrogen fugacity buffer at 500°C. Inflection points in the 0.03 molal proton sorption isotherms (pH infl) at 6.50, 6.24, 5.65, 5.47, 5.31 and 5.55 at temperatures of 50°C, 100°C, 150°C, 200°C, 250°C and 290°C, respectively, were used as estimates of the pristine point of zero charge (pH ppzc) for modeling purposes. These pH infl values parallel 1/2 p K w and agree within the assigned uncertainty (±0.3 pH units) at all temperatures with independent estimates of the pH ppzc calculated from an extension of 88the revised MUSIC model. The surface charging can be adequately described by a one-p K model with a surface protonation constant fitted to the pH infl values, and giving the standard state thermodynamic properties log K H,298=7.00, Δ H 298°=−32.4±0.8 kJ/mol and constant Δ C p=128±16 J K −1 mol −1, with Δ S 298° assumed to be equal to that of rutile protonation (25.5±3.4 J K −1 mol −1. The 0.03 and 0.30 molal proton sorption isotherms also exhibit pHs of common intersection (pH cip) at 6.33, 5.78, 5.37, 4.82, 4.62 and 4.90 at 50°C, 100°C, 150°C, 200°C, 250°C and 290°C, respectively. The difference between the pH cip and pH ppzc≅pH infl values can be related to specific binding of Na + on the negatively charged surface, which increases with increasing temperature, although the pH cip values may also be affected by dissolution of the solid. The electrical double layer model includes a basic Stern layer capacitance, with specific cation and anion binding at the Stern layer, and a fixed diffuse layer capacitance computed from Guoy–Chapman theory. To fit the steepness and asymmetry of the charging curves above the pH ppzc, an additional cation binding constant was invoked, which allows the cation to experience the surface potential. Significant kinetically controlled dissolution of magnetite was observed below the pH ppzc, which may be a result of leaching of Fe 2+ from the surface, to produce a magnetite+hematite assemblage, despite the high hydrogen partial pressures (ca. 10 bars) used in these experiments.

Metal-organic complexes in geochemical processes: temperature dependence of the standard thermodynamic properties of aqueous complexes between metal cations and dicarboxylate ligands

By combining results from regression and correlation methods, standard state thermodynamic properties for aqueous complexes between metal cations and divalent organic acid ligands (oxalate, malonate, succinate, glutarate, and adipate) are evaluated and applied to geochemical processes. Regression of experimental standard-state equilibrium constants with the revised Helgeson–Kirkham–Flowers (HKF) equation of state yields standard partial molal entropies (S̄°) of aqueous metal-organic complexes, which allow determination of thermodynamic properties of the complexes at elevated temperatures. In cases where S̄° is not available from either regression or calorimetric measurement, the values of S̄° can be estimated from a linear correlation between standard partial molal entropies of association (ΔS̄°r) and standard partial molal entropies of aqueous cations (S̄°M). The correlation is independent of cation charge, which makes it possible to predict S̄° for complexes between divalent organic acids and numerous metal cations. Similarly, correlations between standard Gibbs free energies of association of metal-organic complexes (ΔḠ°r) and Gibbs free energies of formation (ΔḠ°f) for divalent metal cations allow estimates of standard-state equilibrium constants where experimental data are not available. These correlations are found to be a function of ligand structure and cation charge. Predicted equilibrium constants for dicarboxylate complexes of numerous cations were included with those for inorganic and other organic complexes to study the effects of dicarboxylate complexes on the speciation of metals and organic acids in oil-field brines. Relatively low concentrations of oxalic and malonic acids affect the speciation of cations more than similar concentrations of succinic, glutaric, and adipic acids. However, the extent to which metal-dicarboxylate complexes contribute to the speciation of dissolved metals depends on the type of dicarboxylic acid ligand; relative concentration of inorganic, mono-, and dicarboxylate ligands; and the type of metal cation. As an example, in the same solution, dicarboxylic acids have a greater influence on the speciation of Fe+2 and Mg+2 than on the speciation of Zn+2 and Mn+2.

Thermodynamics of hydration of Na- and K-clinoptilolite to 300 °C

The hydration state of Na- and K-exchanged clinoptilolite from Castle Creek (Idaho, U.S.A.) has been measured by a pressure titration method to 300 °C and PH2O<30 bars. The water content of clinoptilolite can be predicted as a function of water activity and temperature with the equation: aH2O = [exp[[−ΔHh∘/nRT] + [ΔSh∘/nR] − 1/nRT· [W1Xh + W2Xh2]− ln(Xa/Xh)]]−1 where T is degrees in Kelvin, ΔHh∘ is the standard molal enthalpy of hydration, ΔSh∘ is the entropy of hydration, Xh and Xa are, respectively, the mole fractions of the hydrous and anhydrous components of the solid solution, W1 and W2 are interaction parameters, n is the maximum number of moles of H2O per formula unit (based on 12 oxygens), and R is the gas constant. This equation can be used to locate clinoptilolite-H2O isohydrons in aH2O-T space below the liquid-vapor equilibrium curve of water. The standard molal Gibbs free energy of hydration is −47.62 ± 5.52 kJ/mol H2O and −5.40 ± 2.71 kJ/mol H2O for the Na- and K-clinoptilolite, respectively. These standard-state thermodynamic properties of clinoptilolite hydration are in good agreement with previous data at low H2O pressures. The experiments indicate that clinoptilolite progressively dehydrates with increasing temperature at pressures along the liquid-vapor equilibrium curve. Kinetic data above 150 °C show that clinoptilolite dehydration and hydration reactions are fast and reversible and that steady-state hydration states are attained in minutes.

Critical Evaluation and Selection of Standard State Thermodynamic Properties for Chromium Metal and Its Aqueous Ions, Hydrolysis Species, Oxides, and Hydroxides

This review critically evaluates the reported thermodynamic data on chromium metal, oxides, hydroxides, free aqueous ions, and hydrolysis species. Several discrepancies and inconsistencies have been uncovered and resolved to improve equilibrium calculations for chemical modeling and related engineering purposes. A revised set of data is derived from evaluation of electrochemical measurements, silver chromate solubility measurements, and auxiliary post-1980 data, reevaluation of earlier data, and reconsideration of the path for the thermodynamic network. The recommended thermodynamic values for Cr(cr), C , C , Cr , Cr2 , Cr2O3(cr), CrO3(cr), FeCr2O4(cr), CrCl2(cr), CrCl3(cr), and KFe3(CrO4)2(OH)6(cr) at 25 °C, 1 bar, and infinite dilution are given.

Solubility and transport of platinum-group elements in supercritical fluids: summary and estimates of thermodynamic properties for ruthenium, rhodium, palladium, and platinum solids, aqueous ions, and complexes to 1000°C and 5 kbar

Several correlation methods are used to estimate data and equation-of-state parameters that permit calculation of standard state thermodynamic properties at high pressures and temperatures for metals, oxides, and sulfides, as well as ions, and aqueous chloride, hydroxide, and sulfate complexes of Ru +2, Ru +3, Rh +2, Rh +3, Pd +2, and Pt +2. Estimates are based on a critical review of data from the literature at 25°C and 1 bar. The combined data for 14 minerals, 6 cations, and 56 aqueous complexes provide a foundation for quantitative predictions of aqueous speciation of these platinum group elements (PGE), as well as platinum group mineral (PGM) solubilities as functions of pH, oxidation state, and chloride and sulfate content of geologic fluids at temperatures to 1000°C and pressures to 5 kbar. Therefore, these estimates are the first to address PGE speciation at the pressure and temperatures of most PGM deposits. Comparisons are made to other theoretical predictions of platinum-group element (PGE) complex formation in aqueous solutions and to pertinent experimental data. We conclude that Pd-chloride complexes may be less stable at lower temperatures than previously predicted by other investigators, but that Pt-chloride complexes may be considerably more stable.

Experimental study of dissociation of HCl from 350 to 500°C and from 500 to 2500 bars: Thermodynamic properties of HCl°(aq)

New values of the dissociation constants of HCl° referring to low density supercritical solutions and near-critical temperatures of water (350–500°C and 500–2500 bars) have been obtained based on comparison of AgCl(s) solubility in NaCl or KCl solutions with Ag(s) solubility in HCl + NaCl or KCl solutions at controlled hydrogen fugacities. During the course of this study the thermodynamic properties of AgCls− were refined with the aid of the revised HKF equation of state (Tanger and Helgeson, 1988). The dissociation constants of HCl° obtained in the present work are higher than that found from electrical conductance measurements (Frantz and Marshall, 1984) by more than an order of magnitude at pressures of about 500 bars, but the difference becomes smaller as the pressure increases. Both sets of dissociation constants agree well at high pressures where the isothermal compressibility of water is less than about 1.42·10−4 bar−1.To reliably compare experimental data obtained by different methods, the Redlikh-Kwong equation of state was applied to available literature data as well as to the results of this study. Finally, the standard state thermodynamic properties and HKF parameters for HCl°(aq) were established. These results allow extrapolation of the thermodynamic properties of HCl°(aq) and consequently the HCl dissociation constant up to 700°C and 5000 bars.